# Petrial great stellated dodecahedron

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Petrial great stellated dodecahedron
Rank3
TypeRegular
SpaceSpherical
Notation
Schläfli symbol${\displaystyle \{5/2,3\}^\pi}$
${\displaystyle \{10/3,3\}_{5/2}}$[1]
Elements
Faces6 skew decagons
Edges30
Vertices20
Vertex figureTriangle
Related polytopes
RegimentGissid
Petrie dualGreat stellated dodecahedron
ConjugatePetrial dodecahedron
Convex hullDodecahedron
Abstract properties
Flag count120
Euler characteristic-4
Schläfli type{10,3}
Topological properties
OrientableNo
Genus6
Properties
ConvexNo

The petrial great stellated dodecahedron is a regular skew polyhedron and is the Petrie dual of the great stellated dodecahedron, and so it shares both of its vertices and edges with the great stellated dodecahedron. It consists of 6 skew decagrams and has an Euler characteristic of -4.

## Vertex coordinates

The vertices of the petrial great stellated dodecahedron are identical to those of the great stellated dodecahedron, which is the regiment colonel.

## Related polyhedra

The rectification of the petrial great stellated dodecahedron is the great icosihemidodecahedron, which is uniform.